Against the Gods: The Remarkable Story of Risk (32 page)

Although Quetelet continued to work at the Royal Observatory in
Brussels after he returned from Paris in 1820, he also carried on research
relating to French population statistics and started to plan for the
approaching census of 1829. In 1827, he published a monograph titled
"Researches on population, births, deaths, prisons, and poor houses,
etc. in the Kingdom of the Low Countries," in which he criticized the
procedures used in gathering and analyzing social statistics. Quetelet
was eager to apply a method that Laplace had developed back in the
1780s to estimate France's population. Laplace's method called for taking a random sample from a diversified group of thirty departements and
using the sample as the basis for estimating the total population.

A colleague soon persuaded Quetelet to abandon that approach.
The problem was that the officials in charge of the French census
would have no way of knowing how representative their sample might
be. Each locality had certain customs and conventions that influenced
the birth rate. Furthermore, as Halley and Price had discovered, the
representative quality of a survey even in a small area could be affected
by movements of the population. Unlike Enobarbus, Quetelet found
too much variety in the French sociological structure for anyone to
generalize on the basis of a limited sample. A complete census of France
was decided upon.

This experience led Quetelet to begin using social measurement in a
search to explain why such differences exist among people and placeswhence the variety that adds the spice? If the differences were random,
the data would look about the same each time a sample was taken; if the
differences were systematic, each sample would look different from the
others.

This idea set Quetelet off on a measurement spree, which Stigler
describes as follows:

He examined birth and death rates by month and city, by temperature,
and by time of day.... He investigated mortality by age, by profession,
by locality, by season, in prisons, and in hospitals. He considered ...
height, weight, growth rate, and strength ... [and developed] statistics
on drunkenness, insanity, suicides, and crime.13

The result was A Treatise on Man and the Development of His Faculties,
which was first published in French in 1835 and subsequently translated
into English. The French expression Quetelet chose for "faculties" was
"physique social." This work established Quetelet's reputation. The author
of a three-part review of it in a leading scholarly journal remarked, "We
consider the appearance of these volumes as forming an epoch in the literary history of civilization."14

The book consisted of more than just dry statistics and plodding
text. Quetelet gave it a hero who lives to this very day: l'homme moyen,
or the average man. This invention captured the public imagination
and added to Quetelet's growing fame.

Quetelet aimed to define the characteristics of the average man (or
woman in some instances), who then became the model of the particular group from which he was drawn, be it criminals, drunks, soldiers,
or dead people. Quetelet even speculated that "If an individual at any
epoch of society possessed all the qualities of the average man, he
would represent all that is great, good, or beautiful."15

Not everyone agreed. One of the harshest critics of Quetelet's
book was Antoine-Augustin Cournot, a famous mathematician and
economist, and an authority on probability. Unless we observe the rules
of probability, Cournot maintained, "we cannot get a clear idea of the
precision of measurements made in the sciences of observation ... or of
the conditions leading to the success of commercial enterprises."16
Cournot ridiculed the concept of the average man. An average of all the sides of a bunch of right triangles, he argued, would not be a right
triangle, and a totally average man would not be a man but some kind
of monstrosity.

Quetelet was undeterred. He was convinced that he could identify
the average man for any age, occupation, location, or ethnic origin.
Moreover, he claimed that he could find a method to predict why a
given individual belonged in one group rather than in another. This
was a novel step, for no one up to that point had dared to use mathematics and statistics to separate cause and effect. "[E]ffects are proportional to causes," he wrote, and then went on to italicize these words:
"The greater the number of individuals observed, the more do peculiarities,
whether physical or moral, become effaced, and allow the general facts to predominate, by which society exists and is preserved."" By 1836, Quetelet had
expanded these notions into a book on the application of probability to
the "moral and political sciences."

Quetelet's study of causes and effects makes for fascinating reading.
For example, he carried out an extended analysis of the factors that
influence rates of conviction among people accused of crimes. An average of 61.4% of all people accused were convicted, but the probability
was less than 50% that they would be convicted for crimes against persons while it was over 60% that they would be convicted for crimes
against property. The probability of conviction was less than 61.4% if
the accused was a woman older than thirty who voluntarily appeared to
stand trial instead of running away and who was literate and well educated. Quetelet also sought to determine whether deviations from the
61.4% average were significant or random: he sought moral certainty in
the trials of the immoral.

Quetelet saw bell curves everywhere he looked. In almost every
instance, the "errors," or deviations from the average, obediently distributed themselves according to the predictions of Laplace and Gaussin normal fashion, falling symmetrically along both sides of the average.
That beautifully balanced array, with the peak at the average, was what
convinced Quetelet of the validity of his beloved average man. It lay
behind all the inferences he developed from his statistical investigations.

In one experiment, for example, Quetelet took chest measurements
on 5,738 Scottish soldiers. He concocted a normal distribution for the
group and then compared the actual result with the theoretical result.
The fit was almost perfect.18

It had already been demonstrated that Gaussian normal distributions
are typical throughout nature; now they appeared to be rooted in the
social structures and the physical attributes of human beings. Thus,
Quetelet concluded that the close fit to a normal distribution for the
Scottish soldiers signified that the deviations around the average were
random rather than the result of any systematic differences within the
group. The group, in other words, was essentially homogeneous, and the
average Scottish soldier was fully representative of all Scottish soldiers.
Cleopatra was a woman before all else.

One of Quetelet's studies, however, revealed a less than perfect fit
with the normal distribution. His analysis of the heights of 100,000
French conscripts revealed that too many of them fell in the shortest
class for the distribution to be normal. Since being too short was an
excuse for exemption from service, Quetelet asserted that the measurements must have been distorted by fraud in order to accommodate
draft-dodgers.

Cournot's remark that the average man would be some sort of
monstrosity reflected his misgivings about applying probability theory
to social as opposed to natural data. Human beings, he argued, lend
themselves to a bewildering variety of classifications. Quetelet believed
that a normally distributed set of human measurements implied only
random differences among the sample of people he was examining.
But Cournot suspected that the differences might not be random.
Consider, for example, how one might classify the number of male
births in any one year: by age of parents, by geographical location, by
days of the week, by ethnic origin, by weight, by time in gestation, by
color of eyes, or by length of middle fingers, just to name a few possibilities. How, then, could you state with any confidence which baby
was the average baby? Cournot claimed that it would be impossible to
determine which data were significant and which were nothing more
than the result of chance: "[T]he same size deviation [from the average]
may lead to many different judgments."19 What Cournot did not mention, but what modern statisticians know well, is that most human measurements reflect differences in nutrition, which means that they tend
to reflect differences in social status as well.

Today, statisticians refer to the practice that stirred Cournot's misgivings as "data mining." They say that if you torture the data long
enough, the numbers will prove anything you want. Cournot felt that Quetelet was on dangerous ground in drawing such broad generalizations from a limited number of observations. A second set of observations drawn from a group of the same size could just as likely turn up a
different pattern from the first.

There is no doubt that Quetelet's infatuation with the normal distribution led him to claim more than he should have. Nevertheless, his
analysis was hugely influential at the time. A famous mathematician
and economist of a later age, Francis Ysidro Edgeworth, coined the
term "Quetelismus" to describe the growing popularity of discovering
normal distributions in places where they did not exist or that failed to
meet the conditions that identify genuine normal distributions. 20

When Galton first came upon Quetelet's work in 1863, he was
deeply impressed. "An Average is but a solitary fact," he wrote, "whereas
if a single other fact be added to it, an entire Normal Scheme, which
nearly corresponds to the observed one, starts potentially into existence.
Some people hate the very name of statistics, but I find them full of
beauty and interest."21

Galton was enthralled by Quetelet's finding that "the very curious
theoretical law of the deviation from the average"-the normal distribution-was ubiquitous, especially in such measurements as body
height and chest measurements.22 Galton himself had found bell curves
in the record of 7,634 grades in mathematics for Cambridge students
taking their final exam for honors in mathematics, ranging from highest
to "one can hardly say what depth."23 He found similar statistical patterns in exam grades among the applicants for admission to the Royal
Military College at Sandhurst.

The aspect of the bell curve that impressed Galton most was its
indication that certain data belonged together and could be analyzed as
a relatively homogeneous entity. The opposite would then also be
true: absence of the normal distribution would suggest "dissimilar systems." Galton was emphatic: "This presumption is never found to be
belled.""

But it was differences, not homogeneity, that Galton was pursuingCleopatra, not the woman. In developing his new field of study,
eugenics, he searched for differences even within groups whose mea surable features seemed to fall into a normal distribution. His objective
was to classify people by "natural ability," by which he meant

... those qualities of intellect and disposition, which urge and qualify a man to perform acts that lead to reputation.... I mean a nature
which, when left to itself, will, urged by an inherent stimulus, climb
the path that leads to eminence, and has strength to reach the summit.
... [M]en who achieve eminence, and those who are naturally capable, are, to a large extent, identical. "25

Galton began with the facts. During the years 1866 to 1869, he collected masses of evidence to prove that talent and eminence are hereditary attributes. He then summarized his findings in his most important
work, Hereditary Genius (which includes an appendix on Quetelet's
work, as well as Galton's own caustic appraisal of the typical prickly
Bernoulli personality). The book begins with an estimate of the proportion of the general population that Galton believed he could classify
as "eminent." On the basis of obituaries in the London Times and in a
biographical handbook, he calculated that eminence occurred among
English people past middle age in a ratio of one to every 4,000, or
about 5,000 people in Britain at that time.

Although Galton said that he did not care to occupy himself with
people whose gifts fell below average, he did estimate the number of
"idiots and imbeciles" among Britain's twenty million inhabitants as
50,000, or one in 400, making them about ten times as prevalent as his
eminent citizens.26 But it was the eminent ones he cared about. "I am
sure," he concluded, that no one "can doubt the existence of grand
human animals, of natures preeminently noble, of individuals born to
be kings of men."27 Galton did not ignore "very powerful women" but
decided that, "happy perhaps for the repose of the other sex, such gifted
women are rare."28

Galton was convinced that if height and chest circumference
matched Quetelet's hypotheses, the same should be true of head size,
brain weight, and nerve fibers-and to mental capacity as well. He
demonstrated how well Quetelet's findings agreed with his own estimates of the range of Britons from eminence at one end to idiocy at the
other. He arrived at "the undeniable, but unexpected conclusion, that
eminently gifted men are raised as much above mediocrity as idiots are
depressed below it."29